There are a ton of locks to pick in this game. If you unlock a main door, then Elizabeth will use her hairpin. Otherwise, you will use lock picks. While they may seem rare at the start, you will eventually be picking up a lot of these. There are some cases where they will respawn when you go back and forth between areas. If you're worried about them, save them only for doors you know have collectibles behind them. You can always reload checkpoints to gain your picked locks.
Lock picks are relatively rare and will be expended when Elizabeth picks a lock. Locks also cannot be picked while in combat. To perform a pick hit and elizabeth will approach and pick the lock.